Abstract
We present a novel Bayesian approach to semiotic dynamics, which is a cognitive analog of the naming game model restricted to two conventions. The model introduced in this paper provides a general framework for studying the combined effects of cognitive and social dynamics. The one-shot learning that characterizes the agent dynamics in the basic naming game is replaced by a word-learning process in which agents learn a new word by generalizing from the evidence garnered through pairwise-interactions with other agents. The principle underlying the model is that agents—like humans—can learn from a few positive examples and that such a process is modeled in a Bayesian probabilistic framework. We show that the model presents some analogies with the basic two-convention naming game model but also some relevant differences in the dynamics, which we explain through a geometric analysis of the mean-field equations.
Highlights
A basic question in complexity theory is how the interactions between the units of the system lead to the emergence of ordered states from initially disordered configurations [1, 2]
For the sake of clarity, in analogy with the basic naming game (NG) model, we study the emergence of consensus in the simple situation, in which two names A and B can be used for referring to the same concept C in pair-wise interactions among N agents
We introduce an element of asymmetry between the names A and B, related to the word-learning process: different minimum numbers of examples n∗ex,A = 5 and n∗ex,B = 6 will be used, which are needed by agents to generalize concept C in association with A and B, respectively
Summary
A basic question in complexity theory is how the interactions between the units of the system lead to the emergence of ordered states from initially disordered configurations [1, 2]. This general question can concern different phenomena ranging from phase transitions in condensed matter systems and self-organization in living matter to the appearance of norm conventions and cultural paradigms in social systems. Opinion dynamics and cultural spreading models represent an example of a valuable theoretical framework for a quantitative description of the emergence of social consensus [2]. Language dynamics [11, 12] has provided a set of models describing various phenomena of language competition and language change in a quantitative way, focusing on the mutual interactions of linguistic traits (such as sounds, phonemes, grammatical rules, or the use of languages understood as fixed entities), possibly under the influence of ecological and social factors, modeling such interactions through analogy with biological competition and evolution
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